LMFDB - Embedded newform 592.2.bq.b.465.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [592,2,Mod(65,592)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(592, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 17]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("592.65");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 592 = 2^{4} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	592.bq (of order $18$, degree $6$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.72714379966$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{18})$
Coefficient field:	$\Q(\zeta_{36})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{6} + 1 $ x^12 - x^6 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 74)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			465.2
Root			$0.342020 + 0.939693i$ of defining polynomial
Character	$\chi$	$=$	592.465
Dual form			592.2.bq.b.289.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.326352 + 0.118782i) q^{3} +(2.57176 + 0.453471i) q^{5} +(0.361075 - 2.04776i) q^{7} +(-2.20574 + 1.85083i) q^{9} +O(q^{10})$	\(q+(-0.326352 + 0.118782i) q^{3} +(2.57176 + 0.453471i) q^{5} +(0.361075 - 2.04776i) q^{7} +(-2.20574 + 1.85083i) q^{9} +(2.99810 + 5.19285i) q^{11} +(2.64632 - 3.15377i) q^{13} +(-0.893164 + 0.157489i) q^{15} +(-0.618710 - 0.737350i) q^{17} +(-0.534946 - 1.46975i) q^{19} +(0.125400 + 0.711179i) q^{21} +(5.51705 + 3.18527i) q^{23} +(1.70986 + 0.622339i) q^{25} +(1.02094 - 1.76833i) q^{27} +(-3.51193 + 2.02761i) q^{29} -3.39997i q^{31} +(-1.59525 - 1.33858i) q^{33} +(1.85720 - 5.10261i) q^{35} +(6.07068 + 0.383130i) q^{37} +(-0.489021 + 1.34357i) q^{39} +(7.94502 + 6.66666i) q^{41} -3.76932i q^{43} +(-6.51193 + 3.75967i) q^{45} +(-3.08750 + 5.34771i) q^{47} +(2.51491 + 0.915354i) q^{49} +(0.289501 + 0.167144i) q^{51} +(-1.39401 - 7.90585i) q^{53} +(5.35558 + 14.7143i) q^{55} +(0.349161 + 0.416114i) q^{57} +(-5.02269 + 0.885636i) q^{59} +(-6.25519 + 7.45465i) q^{61} +(2.99362 + 5.18510i) q^{63} +(8.23586 - 6.91071i) q^{65} +(1.83263 - 10.3934i) q^{67} +(-2.17885 - 0.384190i) q^{69} +(10.1503 - 3.69442i) q^{71} +3.55293 q^{73} -0.631940 q^{75} +(11.7162 - 4.26436i) q^{77} +(-2.51098 - 0.442753i) q^{79} +(1.37686 - 7.80856i) q^{81} +(-5.29798 + 4.44553i) q^{83} +(-1.25681 - 2.17686i) q^{85} +(0.905280 - 1.07887i) q^{87} +(-16.0165 + 2.82414i) q^{89} +(-5.50263 - 6.55778i) q^{91} +(0.403856 + 1.10959i) q^{93} +(-0.709264 - 4.02243i) q^{95} +(-14.1175 - 8.15074i) q^{97} +(-16.2241 - 5.90509i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{3} + 12 q^{7} - 6 q^{9}+O(q^{10}) $ 12 * q - 6 * q^3 + 12 * q^7 - 6 * q^9	$ 12 q - 6 q^{3} + 12 q^{7} - 6 q^{9} + 6 q^{11} + 6 q^{13} + 18 q^{19} - 6 q^{21} - 18 q^{25} + 6 q^{27} + 18 q^{29} - 6 q^{33} - 18 q^{35} + 30 q^{37} - 30 q^{39} + 24 q^{41} - 18 q^{45} - 6 q^{47} + 12 q^{49} - 12 q^{53} + 18 q^{55} - 36 q^{57} - 36 q^{61} + 6 q^{63} + 36 q^{65} + 30 q^{67} - 18 q^{69} - 12 q^{71} + 36 q^{75} + 12 q^{77} - 6 q^{79} + 24 q^{81} + 48 q^{83} + 18 q^{85} - 36 q^{87} - 18 q^{89} + 6 q^{91} - 12 q^{93} + 36 q^{97} - 30 q^{99}+O(q^{100}) $ 12 * q - 6 * q^3 + 12 * q^7 - 6 * q^9 + 6 * q^11 + 6 * q^13 + 18 * q^19 - 6 * q^21 - 18 * q^25 + 6 * q^27 + 18 * q^29 - 6 * q^33 - 18 * q^35 + 30 * q^37 - 30 * q^39 + 24 * q^41 - 18 * q^45 - 6 * q^47 + 12 * q^49 - 12 * q^53 + 18 * q^55 - 36 * q^57 - 36 * q^61 + 6 * q^63 + 36 * q^65 + 30 * q^67 - 18 * q^69 - 12 * q^71 + 36 * q^75 + 12 * q^77 - 6 * q^79 + 24 * q^81 + 48 * q^83 + 18 * q^85 - 36 * q^87 - 18 * q^89 + 6 * q^91 - 12 * q^93 + 36 * q^97 - 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/592\mathbb{Z}\right)^\times$.

$n$	$113$	$149$	$223$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−0.326352	+	0.118782i	−0.188419	+	0.0685790i	−0.434507	−	0.900669i	$-0.643077\pi$
$3$	−0.326352	+	0.118782i	−0.188419	+	0.0685790i	0.246087	+	0.969248i	$0.420855\pi$
$4$		0			0
$5$	2.57176	+	0.453471i	1.15013	+	0.202798i	0.716031	−	0.698068i	$-0.245957\pi$
$5$	2.57176	+	0.453471i	1.15013	+	0.202798i	0.434096	+	0.900867i	$0.357068\pi$
$6$		0			0
$7$	0.361075	−	2.04776i	0.136473	−	0.773979i	−0.837349	−	0.546669i	$-0.815896\pi$
$7$	0.361075	−	2.04776i	0.136473	−	0.773979i	0.973822	−	0.227311i	$-0.0729932\pi$
$8$		0			0
$9$	−2.20574	+	1.85083i	−0.735246	+	0.616944i
$10$		0			0
$11$	2.99810	+	5.19285i	0.903960	+	1.56570i	0.822308	+	0.569043i	$0.192686\pi$
$11$	2.99810	+	5.19285i	0.903960	+	1.56570i	0.0816522	+	0.996661i	$0.473980\pi$
$12$		0			0
$13$	2.64632	−	3.15377i	0.733958	−	0.874697i	−0.261949	−	0.965082i	$-0.584365\pi$
$13$	2.64632	−	3.15377i	0.733958	−	0.874697i	0.995907	+	0.0903843i	$0.0288095\pi$
$14$		0			0
$15$	−0.893164	+	0.157489i	−0.230614	+	0.0406634i
$16$		0			0
$17$	−0.618710	−	0.737350i	−0.150059	−	0.178834i	0.685778	−	0.727810i	$-0.259462\pi$
$17$	−0.618710	−	0.737350i	−0.150059	−	0.178834i	−0.835838	+	0.548977i	$0.815018\pi$
$18$		0			0
$19$	−0.534946	−	1.46975i	−0.122725	−	0.337184i	0.863083	−	0.505063i	$-0.168531\pi$
$19$	−0.534946	−	1.46975i	−0.122725	−	0.337184i	−0.985808	+	0.167878i	$0.946308\pi$
$20$		0			0
$21$	0.125400	+	0.711179i	0.0273645	+	0.155192i
$22$		0			0
$23$	5.51705	+	3.18527i	1.15038	+	0.664174i	0.948981	−	0.315334i	$-0.102117\pi$
$23$	5.51705	+	3.18527i	1.15038	+	0.664174i	0.201403	+	0.979508i	$0.435450\pi$
$24$		0			0
$25$	1.70986	+	0.622339i	0.341973	+	0.124468i
$26$		0			0
$27$	1.02094	−	1.76833i	0.196481	−	0.340315i
$28$		0			0
$29$	−3.51193	+	2.02761i	−0.652149	+	0.376519i	−0.789279	−	0.614035i	$-0.789546\pi$
$29$	−3.51193	+	2.02761i	−0.652149	+	0.376519i	0.137130	+	0.990553i	$0.456212\pi$
$30$		0			0
$31$		−	3.39997i		−	0.610653i	−0.952248	−	0.305326i	$-0.901234\pi$
$31$		−	3.39997i		−	0.610653i	0.952248	−	0.305326i	$-0.0987655\pi$
$32$		0			0
$33$	−1.59525	−	1.33858i	−0.277698	−	0.233016i
$34$		0			0
$35$	1.85720	−	5.10261i	0.313924	−	0.862498i
$36$		0			0
$37$	6.07068	+	0.383130i	0.998014	+	0.0629862i
$37$	6.07068	+	0.383130i	0.998014	+	0.0629862i
$38$		0			0
$39$	−0.489021	+	1.34357i	−0.0783060	+	0.215144i
$40$		0			0
$41$	7.94502	+	6.66666i	1.24080	+	1.04116i	0.997461	+	0.0712179i	$0.0226886\pi$
$41$	7.94502	+	6.66666i	1.24080	+	1.04116i	0.243343	+	0.969940i	$0.421756\pi$
$42$		0			0
$43$		−	3.76932i		−	0.574816i	−0.957808	−	0.287408i	$-0.907206\pi$
$43$		−	3.76932i		−	0.574816i	0.957808	−	0.287408i	$-0.0927936\pi$
$44$		0			0
$45$	−6.51193	+	3.75967i	−0.970741	+	0.560458i
$46$		0			0
$47$	−3.08750	+	5.34771i	−0.450359	+	0.780044i	−0.998408	−	0.0564019i	$-0.982037\pi$
$47$	−3.08750	+	5.34771i	−0.450359	+	0.780044i	0.548050	+	0.836446i	$0.315371\pi$
$48$		0			0
$49$	2.51491	+	0.915354i	0.359273	+	0.130765i
$50$		0			0
$51$	0.289501	+	0.167144i	0.0405383	+	0.0234048i
$52$		0			0
$53$	−1.39401	−	7.90585i	−0.191483	−	1.08595i	−0.917339	−	0.398106i	$-0.869668\pi$
$53$	−1.39401	−	7.90585i	−0.191483	−	1.08595i	0.725857	−	0.687846i	$-0.241444\pi$
$54$		0			0
$55$	5.35558	+	14.7143i	0.722146	+	1.98408i
$56$		0			0
$57$	0.349161	+	0.416114i	0.0462475	+	0.0551156i
$58$		0			0
$59$	−5.02269	+	0.885636i	−0.653899	+	0.115300i	−0.490749	−	0.871301i	$-0.663277\pi$
$59$	−5.02269	+	0.885636i	−0.653899	+	0.115300i	−0.163150	+	0.986601i	$0.552166\pi$
$60$		0			0
$61$	−6.25519	+	7.45465i	−0.800895	+	0.954470i	−0.999673	−	0.0255750i	$-0.991858\pi$
$61$	−6.25519	+	7.45465i	−0.800895	+	0.954470i	0.198778	+	0.980045i	$0.436303\pi$
$62$		0			0
$63$	2.99362	+	5.18510i	0.377161	+	0.653262i
$64$		0			0
$65$	8.23586	−	6.91071i	1.02153	−	0.857168i
$66$		0			0
$67$	1.83263	−	10.3934i	0.223892	−	1.26975i	−0.640901	−	0.767624i	$-0.721439\pi$
$67$	1.83263	−	10.3934i	0.223892	−	1.26975i	0.864792	−	0.502130i	$-0.167450\pi$
$68$		0			0
$69$	−2.17885	−	0.384190i	−0.262303	−	0.0462511i
$70$		0			0
$71$	10.1503	−	3.69442i	1.20462	−	0.438447i	0.339787	−	0.940502i	$-0.389645\pi$
$71$	10.1503	−	3.69442i	1.20462	−	0.438447i	0.864835	+	0.502056i	$0.167423\pi$
$72$		0			0
$73$	3.55293			0.415839			0.207920	−	0.978146i	$-0.433331\pi$
$73$	3.55293			0.415839			0.207920	+	0.978146i	$0.433331\pi$
$74$		0			0
$75$	−0.631940			−0.0729701
$76$		0			0
$77$	11.7162	−	4.26436i	1.33519	−	0.485969i
$78$		0			0
$79$	−2.51098	−	0.442753i	−0.282507	−	0.0498136i	0.0305991	−	0.999532i	$-0.490258\pi$
$79$	−2.51098	−	0.442753i	−0.282507	−	0.0498136i	−0.313106	+	0.949718i	$0.601370\pi$
$80$		0			0
$81$	1.37686	−	7.80856i	0.152984	−	0.867617i
$82$		0			0
$83$	−5.29798	+	4.44553i	−0.581529	+	0.487960i	−0.885449	−	0.464737i	$-0.846149\pi$
$83$	−5.29798	+	4.44553i	−0.581529	+	0.487960i	0.303920	+	0.952698i	$0.401704\pi$
$84$		0			0
$85$	−1.25681	−	2.17686i	−0.136320	−	0.236113i
$86$		0			0
$87$	0.905280	−	1.07887i	0.0970562	−	0.115667i
$88$		0			0
$89$	−16.0165	+	2.82414i	−1.69774	+	0.299358i	−0.936905	−	0.349584i	$-0.886323\pi$
$89$	−16.0165	+	2.82414i	−1.69774	+	0.299358i	−0.760838	+	0.648942i	$0.775212\pi$
$90$		0			0
$91$	−5.50263	−	6.55778i	−0.576832	−	0.687442i
$92$		0			0
$93$	0.403856	+	1.10959i	0.0418780	+	0.115059i
$94$		0			0
$95$	−0.709264	−	4.02243i	−0.0727689	−	0.412693i
$96$		0			0
$97$	−14.1175	−	8.15074i	−1.43342	−	0.827583i	−0.436036	−	0.899929i	$-0.643618\pi$
$97$	−14.1175	−	8.15074i	−1.43342	−	0.827583i	−0.997380	+	0.0723469i	$0.976951\pi$
$98$		0			0
$99$	−16.2241	−	5.90509i	−1.63058	−	0.593484i
$100$		0			0
$101$	−2.05124	+	3.55285i	−0.204106	+	0.353521i	−0.949847	−	0.312714i	$-0.898762\pi$
$101$	−2.05124	+	3.55285i	−0.204106	+	0.353521i	0.745742	+	0.666235i	$0.232095\pi$
$102$		0			0
$103$	−9.35250	+	5.39967i	−0.921530	+	0.532045i	−0.884123	−	0.467255i	$-0.845243\pi$
$103$	−9.35250	+	5.39967i	−0.921530	+	0.532045i	−0.0374069	+	0.999300i	$0.511910\pi$
$104$		0			0
$105$			1.88585i			0.184040i
$106$		0			0
$107$	−15.5549	−	13.0521i	−1.50375	−	1.26180i	−0.874930	−	0.484249i	$-0.839093\pi$
$107$	−15.5549	−	13.0521i	−1.50375	−	1.26180i	−0.628823	−	0.777549i	$-0.716463\pi$
$108$		0			0
$109$	2.13072	−	5.85411i	0.204086	−	0.560722i	−0.794851	−	0.606804i	$-0.792451\pi$
$109$	2.13072	−	5.85411i	0.204086	−	0.560722i	0.998938	+	0.0460817i	$0.0146734\pi$
$110$		0			0
$111$	−2.02669	+	0.596055i	−0.192365	+	0.0565750i
$112$		0			0
$113$	2.09726	−	5.76217i	0.197294	−	0.542059i	−0.801112	−	0.598515i	$-0.795758\pi$
$113$	2.09726	−	5.76217i	0.197294	−	0.542059i	0.998405	+	0.0564555i	$0.0179799\pi$
$114$		0			0
$115$	12.7441	+	10.6936i	1.18839	+	0.997181i
$116$		0			0
$117$			11.8543i			1.09593i
$118$		0			0
$119$	−1.73331	+	1.00073i	−0.158893	+	0.0917367i
$120$		0			0
$121$	−12.4772	+	21.6111i	−1.13429	+	1.96464i
$122$		0			0
$123$	−3.38475	−	1.23195i	−0.305193	−	0.111081i
$124$		0			0
$125$	−7.19270	−	4.15271i	−0.643335	−	0.371429i
$126$		0			0
$127$	1.10807	+	6.28420i	0.0983257	+	0.557633i	0.993677	+	0.112273i	$0.0358131\pi$
$127$	1.10807	+	6.28420i	0.0983257	+	0.557633i	−0.895352	+	0.445360i	$0.853076\pi$
$128$		0			0
$129$	0.447729	+	1.23013i	0.0394203	+	0.108307i
$130$		0			0
$131$	−6.71929	−	8.00774i	−0.587067	−	0.699640i	0.387972	−	0.921671i	$-0.373176\pi$
$131$	−6.71929	−	8.00774i	−0.587067	−	0.699640i	−0.975039	+	0.222032i	$0.928731\pi$
$132$		0			0
$133$	−3.20285	+	0.564749i	−0.277722	+	0.0489699i
$134$		0			0
$135$	3.42751	−	4.08475i	0.294993	−	0.351559i
$136$		0			0
$137$	−3.12091	−	5.40557i	−0.266637	−	0.461829i	0.701354	−	0.712813i	$-0.252579\pi$
$137$	−3.12091	−	5.40557i	−0.266637	−	0.461829i	−0.967991	+	0.250984i	$0.919246\pi$
$138$		0			0
$139$	−5.27989	+	4.43035i	−0.447834	+	0.375778i	−0.838632	−	0.544699i	$-0.816644\pi$
$139$	−5.27989	+	4.43035i	−0.447834	+	0.375778i	0.390797	+	0.920477i	$0.372199\pi$
$140$		0			0
$141$	0.372398	−	2.11198i	0.0313616	−	0.177861i
$142$		0			0
$143$	24.3110	+	4.28668i	2.03299	+	0.358470i
$144$		0			0
$145$	−9.95132	+	3.62198i	−0.826412	+	0.300789i
$146$		0			0
$147$	−0.929475			−0.0766618
$148$		0			0
$149$	3.49508			0.286328			0.143164	−	0.989699i	$-0.454272\pi$
$149$	3.49508			0.286328			0.143164	+	0.989699i	$0.454272\pi$
$150$		0			0
$151$	−8.84115	+	3.21791i	−0.719482	+	0.261870i	−0.675706	−	0.737171i	$-0.736161\pi$
$151$	−8.84115	+	3.21791i	−0.719482	+	0.261870i	−0.0437763	+	0.999041i	$0.513939\pi$
$152$		0			0
$153$	2.72942	+	0.481271i	0.220661	+	0.0389085i
$154$		0			0
$155$	1.54179	−	8.74391i	0.123839	−	0.702328i
$156$		0			0
$157$	1.94170	−	1.62928i	0.154964	−	0.130030i	−0.562009	−	0.827131i	$-0.689971\pi$
$157$	1.94170	−	1.62928i	0.154964	−	0.130030i	0.716973	+	0.697101i	$0.245527\pi$
$158$		0			0
$159$	1.39401	+	2.41450i	0.110553	+	0.191483i
$160$		0			0
$161$	8.51472	−	10.1475i	0.671054	−	0.799731i
$162$		0			0
$163$	9.23549	−	1.62847i	0.723379	−	0.127551i	0.200177	−	0.979760i	$-0.435848\pi$
$163$	9.23549	−	1.62847i	0.723379	−	0.127551i	0.523202	+	0.852208i	$0.324737\pi$
$164$		0			0
$165$	−3.49561	−	4.16590i	−0.272133	−	0.324315i
$166$		0			0
$167$	3.56469	+	9.79392i	0.275844	+	0.757876i	0.997822	+	0.0659599i	$0.0210110\pi$
$167$	3.56469	+	9.79392i	0.275844	+	0.757876i	−0.721978	+	0.691916i	$0.756767\pi$
$168$		0			0
$169$	−0.685785	−	3.88928i	−0.0527527	−	0.299175i
$170$		0			0
$171$	3.90021	+	2.25179i	0.298257	+	0.172199i
$172$		0			0
$173$	−2.75312	−	1.00205i	−0.209316	−	0.0761846i	0.235234	−	0.971939i	$-0.424414\pi$
$173$	−2.75312	−	1.00205i	−0.209316	−	0.0761846i	−0.444550	+	0.895754i	$0.646636\pi$
$174$		0			0
$175$	1.89179	−	3.27667i	0.143006	−	0.247693i
$176$		0			0
$177$	1.53397	−	0.885636i	0.115300	−	0.0665685i
$178$		0			0
$179$		−	8.76703i		−	0.655279i	−0.944803	−	0.327639i	$-0.893747\pi$
$179$		−	8.76703i		−	0.655279i	0.944803	−	0.327639i	$-0.106253\pi$
$180$		0			0
$181$	−20.4965	−	17.1986i	−1.52349	−	1.27836i	−0.829750	−	0.558135i	$-0.811517\pi$
$181$	−20.4965	−	17.1986i	−1.52349	−	1.27836i	−0.693740	−	0.720225i	$-0.744038\pi$
$182$		0			0
$183$	1.15591	−	3.17584i	0.0854475	−	0.234765i
$184$		0			0
$185$	15.4386	+	3.73820i	1.13507	+	0.274838i
$186$		0			0
$187$	1.97400	−	5.42352i	0.144353	−	0.396607i
$188$		0			0
$189$	−3.25247	−	2.72915i	−0.236582	−	0.198516i
$190$		0			0
$191$			1.81758i			0.131515i	0.997836	+	0.0657577i	$0.0209464\pi$
$191$			1.81758i			0.131515i	−0.997836	+	0.0657577i	$0.979054\pi$
$192$		0			0
$193$	0.922363	−	0.532526i	0.0663931	−	0.0383321i	−0.466436	−	0.884555i	$-0.654462\pi$
$193$	0.922363	−	0.532526i	0.0663931	−	0.0383321i	0.532829	+	0.846223i	$0.321129\pi$
$194$		0			0
$195$	−1.86692	+	3.23360i	−0.133693	+	0.231563i
$196$		0			0
$197$	14.8064	+	5.38909i	1.05491	+	0.383957i	0.810515	−	0.585718i	$-0.199187\pi$
$197$	14.8064	+	5.38909i	1.05491	+	0.383957i	0.244398	+	0.969675i	$0.421410\pi$
$198$		0			0
$199$	−17.8722	−	10.3185i	−1.26693	−	0.731461i	−0.292523	−	0.956259i	$-0.594495\pi$
$199$	−17.8722	−	10.3185i	−1.26693	−	0.731461i	−0.974406	+	0.224797i	$0.927828\pi$
$200$		0			0
$201$	0.636467	+	3.60958i	0.0448929	+	0.254600i
$202$		0			0
$203$	2.88399	+	7.92370i	0.202417	+	0.556135i
$204$		0			0
$205$	17.4096	+	20.7479i	1.21594	+	1.44910i
$206$		0			0
$207$	−18.0646	+	3.18527i	−1.25557	+	0.221391i
$208$		0			0
$209$	6.02839	−	7.18435i	0.416992	−	0.496952i
$210$		0			0
$211$	3.10070	+	5.37057i	0.213461	+	0.369725i	0.952795	−	0.303613i	$-0.0981931\pi$
$211$	3.10070	+	5.37057i	0.213461	+	0.369725i	−0.739335	+	0.673338i	$0.764860\pi$
$212$		0			0
$213$	−2.87375	+	2.41136i	−0.196906	+	0.165224i
$214$		0			0
$215$	1.70928	−	9.69380i	0.116572	−	0.661112i
$216$		0			0
$217$	−6.96231	−	1.22764i	−0.472633	−	0.0833379i
$218$		0			0
$219$	−1.15951	+	0.422026i	−0.0783521	+	0.0285178i
$220$		0			0
$221$	−3.96274			−0.266563
$222$		0			0
$223$	−0.839150			−0.0561936			−0.0280968	−	0.999605i	$-0.508945\pi$
$223$	−0.839150			−0.0561936			−0.0280968	+	0.999605i	$0.508945\pi$
$224$		0			0
$225$	−4.92335	+	1.79195i	−0.328224	+	0.119464i
$226$		0			0
$227$	−6.42458	−	1.13283i	−0.426415	−	0.0751884i	−0.0436775	−	0.999046i	$-0.513907\pi$
$227$	−6.42458	−	1.13283i	−0.426415	−	0.0751884i	−0.382737	+	0.923857i	$0.625019\pi$
$228$		0			0
$229$	1.14680	−	6.50380i	0.0757824	−	0.429784i	−0.923185	−	0.384355i	$-0.874424\pi$
$229$	1.14680	−	6.50380i	0.0757824	−	0.429784i	0.998968	−	0.0454281i	$-0.0144652\pi$
$230$		0			0
$231$	−3.31709	+	2.78336i	−0.218248	+	0.183132i
$232$		0			0
$233$	11.3047	+	19.5803i	0.740594	+	1.28275i	0.952225	+	0.305396i	$0.0987889\pi$
$233$	11.3047	+	19.5803i	0.740594	+	1.28275i	−0.211632	+	0.977349i	$0.567878\pi$
$234$		0			0
$235$	−10.3654	+	12.3530i	−0.676161	+	0.805818i
$236$		0			0
$237$	0.872054	−	0.153767i	0.0566460	−	0.00998822i
$238$		0			0
$239$	11.0221	+	13.1357i	0.712962	+	0.849675i	0.993927	−	0.110043i	$-0.0350988\pi$
$239$	11.0221	+	13.1357i	0.712962	+	0.849675i	−0.280965	+	0.959718i	$0.590654\pi$
$240$		0			0
$241$	1.94526	+	5.34455i	0.125305	+	0.344273i	0.986444	−	0.164096i	$-0.0524708\pi$
$241$	1.94526	+	5.34455i	0.125305	+	0.344273i	−0.861139	+	0.508369i	$0.830249\pi$
$242$		0			0
$243$	1.54189	+	8.74449i	0.0989122	+	0.560959i
$244$		0			0
$245$	6.05267	+	3.49451i	0.386691	+	0.223256i
$246$		0			0
$247$	−6.05089	−	2.20235i	−0.385009	−	0.140132i
$248$		0			0
$249$	1.20095	−	2.08011i	0.0761074	−	0.131822i
$250$		0			0
$251$	21.9528	−	12.6745i	1.38565	−	0.800006i	0.392829	−	0.919611i	$-0.371496\pi$
$251$	21.9528	−	12.6745i	1.38565	−	0.800006i	0.992821	+	0.119606i	$0.0381630\pi$
$252$		0			0
$253$			38.1990i			2.40155i
$254$		0			0
$255$	0.668734	+	0.561134i	0.0418777	+	0.0351396i
$256$		0			0
$257$	1.76857	−	4.85911i	0.110320	−	0.303103i	−0.872231	−	0.489094i	$-0.837327\pi$
$257$	1.76857	−	4.85911i	0.110320	−	0.303103i	0.982551	+	0.185991i	$0.0595496\pi$
$258$		0			0
$259$	2.97653	−	12.2929i	0.184953	−	0.763847i
$260$		0			0
$261$	3.99362	−	10.9724i	0.247199	−	0.679173i
$262$		0			0
$263$	−7.40923	−	6.21708i	−0.456873	−	0.383362i	0.385106	−	0.922872i	$-0.374165\pi$
$263$	−7.40923	−	6.21708i	−0.456873	−	0.383362i	−0.841979	+	0.539511i	$0.818609\pi$
$264$		0			0
$265$		−	20.9641i		−	1.28782i
$266$		0			0
$267$	4.89155	−	2.82414i	0.299358	−	0.172834i
$268$		0			0
$269$	11.9383	−	20.6777i	0.727889	−	1.26074i	−0.229885	−	0.973218i	$-0.573835\pi$
$269$	11.9383	−	20.6777i	0.727889	−	1.26074i	0.957774	−	0.287523i	$-0.0928316\pi$
$270$		0			0
$271$	17.2047	+	6.26199i	1.04511	+	0.380389i	0.806815	−	0.590804i	$-0.201189\pi$
$271$	17.2047	+	6.26199i	1.04511	+	0.380389i	0.238295	+	0.971193i	$0.423411\pi$
$272$		0			0
$273$	2.57474	+	1.48653i	0.155830	+	0.0899687i
$274$		0			0
$275$	1.89462	+	10.7449i	0.114250	+	0.647942i
$276$		0			0
$277$	−6.06459	−	16.6623i	−0.364386	−	1.00114i	−0.977461	−	0.211117i	$-0.932290\pi$
$277$	−6.06459	−	16.6623i	−0.364386	−	1.00114i	0.613075	−	0.790025i	$-0.289932\pi$
$278$		0			0
$279$	6.29278	+	7.49944i	0.376739	+	0.448980i
$280$		0			0
$281$	−15.0167	+	2.64786i	−0.895824	+	0.157958i	−0.602560	−	0.798074i	$-0.705853\pi$
$281$	−15.0167	+	2.64786i	−0.895824	+	0.157958i	−0.293264	+	0.956032i	$0.594741\pi$
$282$		0			0
$283$	−15.7182	+	18.7322i	−0.934350	+	1.11351i	0.0589858	+	0.998259i	$0.481213\pi$
$283$	−15.7182	+	18.7322i	−0.934350	+	1.11351i	−0.993336	+	0.115256i	$0.963231\pi$
$284$		0			0
$285$	0.709264	+	1.22848i	0.0420132	+	0.0727689i
$286$		0			0
$287$	16.5205	−	13.8623i	0.975172	−	0.818266i
$288$		0			0
$289$	2.79114	−	15.8293i	0.164184	−	0.931136i
$290$		0			0
$291$	5.57544	+	0.983100i	0.326838	+	0.0576303i
$292$		0			0
$293$	−11.8143	+	4.30005i	−0.690199	+	0.251212i	−0.663220	−	0.748424i	$-0.730811\pi$
$293$	−11.8143	+	4.30005i	−0.690199	+	0.251212i	−0.0269784	+	0.999636i	$0.508589\pi$
$294$		0			0
$295$	−13.3188			−0.775450
$296$		0			0
$297$	12.2436			0.710443
$298$		0			0
$299$	24.6455	−	8.97022i	1.42529	−	0.518761i
$300$		0			0
$301$	−7.71866	−	1.36101i	−0.444896	−	0.0784472i
$302$		0			0
$303$	0.247409	−	1.40313i	0.0142133	−	0.0806076i
$304$		0			0
$305$	−19.4673	+	16.3350i	−1.11470	+	0.935341i
$306$		0			0
$307$	4.70103	+	8.14242i	0.268302	+	0.464713i	0.968423	−	0.249311i	$-0.0802042\pi$
$307$	4.70103	+	8.14242i	0.268302	+	0.464713i	−0.700122	+	0.714024i	$0.746871\pi$
$308$		0			0
$309$	2.41082	−	2.87310i	0.137147	−	0.163445i
$310$		0			0
$311$	15.8568	−	2.79599i	0.899158	−	0.158546i	0.295082	−	0.955472i	$-0.404653\pi$
$311$	15.8568	−	2.79599i	0.899158	−	0.158546i	0.604077	+	0.796926i	$0.293542\pi$
$312$		0			0
$313$	0.370220	+	0.441211i	0.0209261	+	0.0249387i	0.776406	−	0.630233i	$-0.217041\pi$
$313$	0.370220	+	0.441211i	0.0209261	+	0.0249387i	−0.755480	+	0.655172i	$0.772596\pi$
$314$		0			0
$315$	5.34759	+	14.6924i	0.301302	+	0.827822i
$316$		0			0
$317$	2.04083	+	11.5741i	0.114624	+	0.650067i	0.986935	+	0.161116i	$0.0515093\pi$
$317$	2.04083	+	11.5741i	0.114624	+	0.650067i	−0.872311	+	0.488951i	$0.837380\pi$
$318$		0			0
$319$	−21.0582	−	12.1580i	−1.17903	−	0.680715i
$320$		0			0
$321$	6.62675	+	2.41194i	0.369869	+	0.134621i
$322$		0			0
$323$	−0.752745	+	1.30379i	−0.0418838	+	0.0725449i
$324$		0			0
$325$	6.48757	−	3.74560i	0.359865	−	0.207768i
$326$		0			0
$327$			2.16359i			0.119647i
$328$		0			0
$329$	9.83600	+	8.25338i	0.542276	+	0.455024i
$330$		0			0
$331$	−4.83530	+	13.2849i	−0.265772	+	0.730202i	0.732980	+	0.680250i	$0.238129\pi$
$331$	−4.83530	+	13.2849i	−0.265772	+	0.730202i	−0.998752	+	0.0499518i	$0.984093\pi$
$332$		0			0
$333$	−14.0994	+	10.3907i	−0.772645	+	0.569409i
$334$		0			0
$335$	9.42620	−	25.8983i	0.515008	−	1.41497i
$336$		0			0
$337$	8.21240	+	6.89102i	0.447358	+	0.375378i	0.838454	−	0.544972i	$-0.183460\pi$
$337$	8.21240	+	6.89102i	0.447358	+	0.375378i	−0.391096	+	0.920350i	$0.627904\pi$
$338$		0			0
$339$			2.12961i			0.115665i
$340$		0			0
$341$	17.6555	−	10.1934i	0.956101	−	0.552005i
$342$		0			0
$343$	10.0602	−	17.4248i	0.543200	−	0.940850i
$344$		0			0
$345$	−5.42927	−	1.97609i	−0.292302	−	0.106389i
$346$		0			0
$347$	6.10989	+	3.52754i	0.327996	+	0.189368i	0.654951	−	0.755671i	$-0.272689\pi$
$347$	6.10989	+	3.52754i	0.327996	+	0.189368i	−0.326955	+	0.945040i	$0.606023\pi$
$348$		0			0
$349$	4.45331	+	25.2560i	0.238380	+	1.35192i	0.835376	+	0.549679i	$0.185250\pi$
$349$	4.45331	+	25.2560i	0.238380	+	1.35192i	−0.596996	+	0.802244i	$0.703639\pi$
$350$		0			0
$351$	−2.87514	−	7.89939i	−0.153464	−	0.421638i
$352$		0			0
$353$	4.22017	+	5.02940i	0.224617	+	0.267688i	0.866570	−	0.499056i	$-0.166320\pi$
$353$	4.22017	+	5.02940i	0.224617	+	0.267688i	−0.641953	+	0.766744i	$0.721875\pi$
$354$		0			0
$355$	27.7795	−	4.89828i	1.47438	−	0.259974i
$356$		0			0
$357$	0.446801	−	0.532477i	0.0236472	−	0.0281817i
$358$		0			0
$359$	9.92813	+	17.1960i	0.523987	+	0.907572i	0.999610	+	0.0279226i	$0.00888919\pi$
$359$	9.92813	+	17.1960i	0.523987	+	0.907572i	−0.475623	+	0.879649i	$0.657777\pi$
$360$		0			0
$361$	12.6808	−	10.6405i	0.667413	−	0.560026i
$362$		0			0
$363$	1.50493	−	8.53487i	0.0789883	−	0.447965i
$364$		0			0
$365$	9.13730	+	1.61115i	0.478268	+	0.0843315i
$366$		0			0
$367$	−20.2967	+	7.38739i	−1.05948	+	0.385619i	−0.812233	−	0.583334i	$-0.801748\pi$
$367$	−20.2967	+	7.38739i	−1.05948	+	0.385619i	−0.247246	+	0.968953i	$0.579526\pi$
$368$		0			0
$369$	−29.8635			−1.55463
$370$		0			0
$371$	−16.6926			−0.866637
$372$		0			0
$373$	29.3944	−	10.6987i	1.52198	−	0.553956i	0.560340	−	0.828263i	$-0.310670\pi$
$373$	29.3944	−	10.6987i	1.52198	−	0.553956i	0.961642	+	0.274306i	$0.0884482\pi$
$374$		0			0
$375$	2.84062	+	0.500878i	0.146689	+	0.0258652i
$376$		0			0
$377$	−2.89909	+	16.4415i	−0.149311	+	0.846782i
$378$		0			0
$379$	15.3668	−	12.8943i	0.789339	−	0.662334i	−0.156243	−	0.987719i	$-0.549938\pi$
$379$	15.3668	−	12.8943i	0.789339	−	0.662334i	0.945582	+	0.325384i	$0.105494\pi$
$380$		0			0
$381$	−1.10807	−	1.91924i	−0.0567684	−	0.0983257i
$382$		0			0
$383$	−10.6054	+	12.6391i	−0.541913	+	0.645826i	−0.965615	−	0.259975i	$-0.916286\pi$
$383$	−10.6054	+	12.6391i	−0.541913	+	0.645826i	0.423703	+	0.905801i	$0.360730\pi$
$384$		0			0
$385$	32.0652	−	5.65395i	1.63419	−	0.288152i
$386$		0			0
$387$	6.97639	+	8.31414i	0.354630	+	0.422631i
$388$		0			0
$389$	0.282656	+	0.776592i	0.0143312	+	0.0393748i	0.946652	−	0.322258i	$-0.104442\pi$
$389$	0.282656	+	0.776592i	0.0143312	+	0.0393748i	−0.932321	+	0.361632i	$0.882220\pi$
$390$		0			0
$391$	−1.06479	−	6.03875i	−0.0538490	−	0.305393i
$392$		0			0
$393$	3.14403	+	1.81521i	0.158595	+	0.0915651i
$394$		0			0
$395$	−6.25687	−	2.27731i	−0.314817	−	0.114584i
$396$		0			0
$397$	−4.52451	+	7.83669i	−0.227079	+	0.393312i	−0.956941	−	0.290282i	$-0.906251\pi$
$397$	−4.52451	+	7.83669i	−0.227079	+	0.393312i	0.729862	+	0.683594i	$0.239584\pi$
$398$		0			0
$399$	0.978174	−	0.564749i	0.0489699	−	0.0282728i
$400$		0			0
$401$		−	13.1254i		−	0.655452i	−0.944773	−	0.327726i	$-0.893718\pi$
$401$		−	13.1254i		−	0.655452i	0.944773	−	0.327726i	$-0.106282\pi$
$402$		0			0
$403$	−10.7227	−	8.99742i	−0.534136	−	0.448194i
$404$		0			0
$405$	7.08191	−	19.4574i	0.351903	−	0.966845i
$406$		0			0
$407$	16.2110	+	32.6728i	0.803547	+	1.61953i
$408$		0			0
$409$	2.70223	−	7.42432i	0.133617	−	0.367109i	−0.854783	−	0.518986i	$-0.826310\pi$
$409$	2.70223	−	7.42432i	0.133617	−	0.367109i	0.988399	+	0.151877i	$0.0485318\pi$
$410$		0			0
$411$	1.66060	+	1.39341i	0.0819113	+	0.0687318i
$412$		0			0
$413$			10.6050i			0.521840i
$414$		0			0
$415$	−15.6411	+	9.03037i	−0.767789	+	0.443283i
$416$		0			0
$417$	1.19685	−	2.07301i	0.0586102	−	0.101516i
$418$		0			0
$419$	−30.0521	−	10.9381i	−1.46814	−	0.534361i	−0.520548	−	0.853832i	$-0.674272\pi$
$419$	−30.0521	−	10.9381i	−1.46814	−	0.534361i	−0.947596	+	0.319472i	$0.896494\pi$
$420$		0			0
$421$	−4.86073	−	2.80634i	−0.236897	−	0.136773i	0.376853	−	0.926273i	$-0.377006\pi$
$421$	−4.86073	−	2.80634i	−0.236897	−	0.136773i	−0.613750	+	0.789501i	$0.710340\pi$
$422$		0			0
$423$	−3.08750	−	17.5101i	−0.150120	−	0.851370i
$424$		0			0
$425$	−0.599028	−	1.64581i	−0.0290571	−	0.0798337i
$426$		0			0
$427$	13.0067	+	15.5008i	0.629439	+	0.750136i
$428$		0			0
$429$	−8.44311	+	1.48875i	−0.407637	+	0.0718775i
$430$		0			0
$431$	12.8250	−	15.2842i	0.617757	−	0.736214i	−0.362926	−	0.931818i	$-0.618222\pi$
$431$	12.8250	−	15.2842i	0.617757	−	0.736214i	0.980683	+	0.195604i	$0.0626666\pi$
$432$		0			0
$433$	7.91046	+	13.7013i	0.380152	+	0.658443i	0.991084	−	0.133240i	$-0.0425382\pi$
$433$	7.91046	+	13.7013i	0.380152	+	0.658443i	−0.610931	+	0.791684i	$0.709205\pi$
$434$		0			0
$435$	2.81740	−	2.36408i	0.135084	−	0.113349i
$436$		0			0
$437$	1.73023	−	9.81263i	0.0827682	−	0.469402i
$438$		0			0
$439$	−3.01674	−	0.531932i	−0.143981	−	0.0253878i	0.101193	−	0.994867i	$-0.467734\pi$
$439$	−3.01674	−	0.531932i	−0.143981	−	0.0253878i	−0.245174	+	0.969479i	$0.578845\pi$
$440$		0			0
$441$	−7.24141	+	2.63566i	−0.344829	+	0.125507i
$442$		0			0
$443$	2.75923			0.131095			0.0655475	−	0.997849i	$-0.479121\pi$
$443$	2.75923			0.131095			0.0655475	+	0.997849i	$0.479121\pi$
$444$		0			0
$445$	−42.4712			−2.01333
$446$		0			0
$447$	−1.14062	+	0.415153i	−0.0539497	+	0.0196361i
$448$		0			0
$449$	−22.3120	−	3.93421i	−1.05297	−	0.185667i	−0.379735	−	0.925095i	$-0.623985\pi$
$449$	−22.3120	−	3.93421i	−1.05297	−	0.185667i	−0.673235	+	0.739428i	$0.735096\pi$
$450$		0			0
$451$	−10.7991	+	61.2446i	−0.508509	+	2.88390i
$452$		0			0
$453$	2.50309	−	2.10034i	0.117606	−	0.0986828i
$454$		0			0
$455$	−11.1777	−	19.3603i	−0.524018	−	0.907626i
$456$		0			0
$457$	−18.9638	+	22.6002i	−0.887089	+	1.05719i	0.110902	+	0.993831i	$0.464626\pi$
$457$	−18.9638	+	22.6002i	−0.887089	+	1.05719i	−0.997991	+	0.0633601i	$0.979818\pi$
$458$		0			0
$459$	−1.93554	+	0.341289i	−0.0903435	+	0.0159300i
$460$		0			0
$461$	2.61917	+	3.12141i	0.121987	+	0.145378i	0.823581	−	0.567198i	$-0.191973\pi$
$461$	2.61917	+	3.12141i	0.121987	+	0.145378i	−0.701594	+	0.712576i	$0.747528\pi$
$462$		0			0
$463$	1.00637	+	2.76497i	0.0467699	+	0.128499i	0.960879	−	0.276970i	$-0.0893303\pi$
$463$	1.00637	+	2.76497i	0.0467699	+	0.128499i	−0.914109	+	0.405469i	$0.867108\pi$
$464$		0			0
$465$	0.535457	+	3.03673i	0.0248312	+	0.140825i
$466$		0			0
$467$	−4.59204	−	2.65121i	−0.212494	−	0.122684i	0.389976	−	0.920825i	$-0.372483\pi$
$467$	−4.59204	−	2.65121i	−0.212494	−	0.122684i	−0.602470	+	0.798142i	$0.705817\pi$
$468$		0			0
$469$	−20.6214	−	7.50558i	−0.952208	−	0.346575i
$470$		0			0
$471$	−0.440147	+	0.762356i	−0.0202809	+	0.0351275i
$472$		0			0
$473$	19.5735	−	11.3008i	0.899992	−	0.519611i
$474$		0			0
$475$		−	2.84599i		−	0.130583i
$476$		0			0
$477$	17.7072	+	14.8581i	0.810759	+	0.680308i
$478$		0			0
$479$	6.11079	−	16.7893i	0.279209	−	0.767121i	−0.718244	−	0.695792i	$-0.755054\pi$
$479$	6.11079	−	16.7893i	0.279209	−	0.767121i	0.997453	−	0.0713293i	$-0.0227241\pi$
$480$		0			0
$481$	17.2733	−	18.1316i	0.787595	−	0.826731i
$482$		0			0
$483$	−1.57346	+	4.32304i	−0.0715948	+	0.196705i
$484$		0			0
$485$	−32.6107	−	27.3637i	−1.48078	−	1.24252i
$486$		0			0
$487$			31.2962i			1.41817i	0.705124	+	0.709084i	$0.250891\pi$
$487$			31.2962i			1.41817i	−0.705124	+	0.709084i	$0.749109\pi$
$488$		0			0
$489$	−2.82059	+	1.62847i	−0.127551	+	0.0736418i
$490$		0			0
$491$	−6.72900	+	11.6550i	−0.303676	+	0.525982i	−0.976966	−	0.213397i	$-0.931547\pi$
$491$	−6.72900	+	11.6550i	−0.303676	+	0.525982i	0.673290	+	0.739379i	$0.264881\pi$
$492$		0			0
$493$	3.66793	+	1.33502i	0.165195	+	0.0601261i
$494$		0			0
$495$	−39.0468	−	22.5437i	−1.75502	−	1.01326i
$496$		0			0
$497$	−3.90024	−	22.1194i	−0.174950	−	0.992189i
$498$		0			0
$499$	−12.5759	−	34.5520i	−0.562974	−	1.54676i	−0.815253	−	0.579104i	$-0.803402\pi$
$499$	−12.5759	−	34.5520i	−0.562974	−	1.54676i	0.252279	−	0.967654i	$-0.418820\pi$
$500$		0			0
$501$	−2.32669	−	2.77284i	−0.103949	−	0.123881i
$502$		0			0
$503$	−6.15105	+	1.08460i	−0.274262	+	0.0483597i	−0.309087	−	0.951034i	$-0.600024\pi$
$503$	−6.15105	+	1.08460i	−0.274262	+	0.0483597i	0.0348257	+	0.999393i	$0.488912\pi$
$504$		0			0
$505$	−6.88641	+	8.20690i	−0.306441	+	0.365202i
$506$		0			0
$507$	0.685785	+	1.18781i	0.0304568	+	0.0527527i
$508$		0			0
$509$	−6.29668	+	5.28355i	−0.279096	+	0.234189i	−0.771580	−	0.636132i	$-0.780533\pi$
$509$	−6.29668	+	5.28355i	−0.279096	+	0.234189i	0.492484	+	0.870321i	$0.336089\pi$
$510$		0			0
$511$	1.28287	−	7.27554i	0.0567510	−	0.321851i
$512$		0			0
$513$	−3.14515	−	0.554575i	−0.138862	−	0.0244851i
$514$		0			0
$515$	−26.5010	+	9.64558i	−1.16777	+	0.425035i
$516$		0			0
$517$	−37.0265			−1.62842
$518$		0			0
$519$	1.01751			0.0446638
$520$		0			0
$521$	−20.8518	+	7.58945i	−0.913536	+	0.332500i	−0.755664	−	0.654960i	$-0.772686\pi$
$521$	−20.8518	+	7.58945i	−0.913536	+	0.332500i	−0.157872	+	0.987460i	$0.550463\pi$
$522$		0			0
$523$	13.7427	+	2.42321i	0.600927	+	0.105960i	0.465832	−	0.884873i	$-0.345755\pi$
$523$	13.7427	+	2.42321i	0.600927	+	0.105960i	0.135095	+	0.990833i	$0.456866\pi$
$524$		0			0
$525$	−0.228178	+	1.29406i	−0.00995849	+	0.0564774i
$526$		0			0
$527$	−2.50697	+	2.10360i	−0.109205	+	0.0916340i
$528$		0			0
$529$	8.79187	+	15.2280i	0.382255	+	0.662086i
$530$		0			0
$531$	9.43958	−	11.2496i	0.409643	−	0.488193i
$532$		0			0
$533$	42.0502	−	7.41459i	1.82140	−	0.321161i
$534$		0			0
$535$	−34.0848	−	40.6207i	−1.47362	−	1.75619i
$536$		0			0
$537$	1.04137	+	2.86114i	0.0449384	+	0.123467i
$538$		0			0
$539$	2.78665	+	15.8039i	0.120030	+	0.680722i
$540$		0			0
$541$	20.9379	+	12.0885i	0.900192	+	0.519726i	0.877262	−	0.480011i	$-0.159367\pi$
$541$	20.9379	+	12.0885i	0.900192	+	0.519726i	0.0229292	+	0.999737i	$0.492701\pi$
$542$		0			0
$543$	8.73195	+	3.17817i	0.374724	+	0.136388i
$544$		0			0
$545$	8.13439	−	14.0892i	0.348439	−	0.603514i
$546$		0			0
$547$	32.2382	−	18.6127i	1.37840	−	0.795822i	0.386437	−	0.922316i	$-0.373706\pi$
$547$	32.2382	−	18.6127i	1.37840	−	0.795822i	0.991967	+	0.126494i	$0.0403724\pi$
$548$		0			0
$549$		−	28.0203i		−	1.19588i
$550$		0			0
$551$	4.85878	+	4.07700i	0.206991	+	0.173686i
$552$		0			0
$553$	−1.81330	+	4.98201i	−0.0771095	+	0.211857i
$554$		0			0
$555$	−5.48245	+	0.613867i	−0.232717	+	0.0260572i
$556$		0			0
$557$	0.974054	−	2.67619i	0.0412720	−	0.113394i	−0.917345	−	0.398094i	$-0.869672\pi$
$557$	0.974054	−	2.67619i	0.0412720	−	0.113394i	0.958617	+	0.284700i	$0.0918940\pi$
$558$		0			0
$559$	−11.8876	−	9.97485i	−0.502790	−	0.421891i
$560$		0			0
$561$			2.00445i			0.0846280i
$562$		0			0
$563$	21.5088	−	12.4181i	0.906489	−	0.523362i	0.0271895	−	0.999630i	$-0.491344\pi$
$563$	21.5088	−	12.4181i	0.906489	−	0.523362i	0.879300	+	0.476268i	$0.158011\pi$
$564$		0			0
$565$	8.00663	−	13.8679i	0.336841	−	0.583427i
$566$		0			0
$567$	−15.4929	−	5.63895i	−0.650640	−	0.236813i
$568$		0			0
$569$	−8.80519	−	5.08368i	−0.369133	−	0.213119i	0.303947	−	0.952689i	$-0.401696\pi$
$569$	−8.80519	−	5.08368i	−0.369133	−	0.213119i	−0.673080	+	0.739570i	$0.735029\pi$
$570$		0			0
$571$	−3.25922	−	18.4839i	−0.136394	−	0.773528i	−0.973879	−	0.227068i	$-0.927086\pi$
$571$	−3.25922	−	18.4839i	−0.136394	−	0.773528i	0.837485	−	0.546460i	$-0.184025\pi$
$572$		0			0
$573$	−0.215896	−	0.593170i	−0.00901919	−	0.0247800i
$574$		0			0
$575$	7.45108	+	8.87985i	0.310731	+	0.370315i
$576$		0			0
$577$	−18.5265	+	3.26672i	−0.771267	+	0.135995i	−0.545415	−	0.838166i	$-0.683628\pi$
$577$	−18.5265	+	3.26672i	−0.771267	+	0.135995i	−0.225852	+	0.974162i	$0.572517\pi$
$578$		0			0
$579$	−0.237760	+	0.283351i	−0.00988097	+	0.0117757i
$580$		0			0
$581$	7.19040	+	12.4541i	0.298308	+	0.516685i
$582$		0			0
$583$	36.8745	−	30.9414i	1.52719	−	1.28146i
$584$		0			0
$585$	−5.37558	+	30.4864i	−0.222253	+	1.26046i
$586$		0			0
$587$	−30.2531	−	5.33444i	−1.24868	−	0.220176i	−0.490048	−	0.871696i	$-0.663021\pi$
$587$	−30.2531	−	5.33444i	−1.24868	−	0.220176i	−0.758632	+	0.651520i	$0.774132\pi$
$588$		0			0
$589$	−4.99711	+	1.81880i	−0.205902	+	0.0749423i
$590$		0			0
$591$	−5.47223			−0.225097
$592$		0			0
$593$	6.18887			0.254147			0.127073	−	0.991893i	$-0.459442\pi$
$593$	6.18887			0.254147			0.127073	+	0.991893i	$0.459442\pi$
$594$		0			0
$595$	−4.91147	+	1.78763i	−0.201351	+	0.0732857i
$596$		0			0
$597$	7.05829	+	1.24457i	0.288877	+	0.0509368i
$598$		0			0
$599$	0.183355	−	1.03986i	0.00749169	−	0.0424875i	−0.980833	−	0.194852i	$-0.937578\pi$
$599$	0.183355	−	1.03986i	0.00749169	−	0.0424875i	0.988324	+	0.152364i	$0.0486886\pi$
$600$		0			0
$601$	−11.9378	+	10.0170i	−0.486954	+	0.408603i	−0.852933	−	0.522020i	$-0.825179\pi$
$601$	−11.9378	+	10.0170i	−0.486954	+	0.408603i	0.365979	+	0.930623i	$0.380734\pi$
$602$		0			0
$603$	15.1941	+	26.3170i	0.618752	+	1.07171i
$604$		0			0
$605$	−41.8883	+	49.9205i	−1.70300	+	2.02956i
$606$		0			0
$607$	31.7497	−	5.59834i	1.28868	−	0.227229i	0.513020	−	0.858377i	$-0.328527\pi$
$607$	31.7497	−	5.59834i	1.28868	−	0.227229i	0.775663	+	0.631147i	$0.217416\pi$
$608$		0			0
$609$	−1.88239	−	2.24335i	−0.0762784	−	0.0909050i
$610$		0			0
$611$	8.69490	+	23.8890i	0.351758	+	0.966447i
$612$		0			0
$613$	−0.968237	−	5.49114i	−0.0391067	−	0.221785i	0.958991	−	0.283436i	$-0.0914745\pi$
$613$	−0.968237	−	5.49114i	−0.0391067	−	0.221785i	−0.998098	+	0.0616512i	$0.980363\pi$
$614$		0			0
$615$	−8.14613	−	4.70317i	−0.328484	−	0.189650i
$616$		0			0
$617$	−3.80891	−	1.38633i	−0.153341	−	0.0558116i	0.264209	−	0.964465i	$-0.414889\pi$
$617$	−3.80891	−	1.38633i	−0.153341	−	0.0558116i	−0.417550	+	0.908654i	$0.637111\pi$
$618$		0			0
$619$	−3.68705	+	6.38616i	−0.148195	+	0.256681i	−0.930560	−	0.366138i	$-0.880680\pi$
$619$	−3.68705	+	6.38616i	−0.148195	+	0.256681i	0.782365	+	0.622820i	$0.214013\pi$
$620$		0			0
$621$	11.2652	−	6.50397i	0.452057	−	0.260995i
$622$		0			0
$623$			33.8176i			1.35487i
$624$		0			0
$625$	−23.5843	−	19.7895i	−0.943370	−	0.791581i
$626$		0			0
$627$	−1.11400	+	3.06069i	−0.0444889	+	0.122232i
$628$		0			0
$629$	−3.47349	−	4.71327i	−0.138497	−	0.187930i
$630$		0			0
$631$	−2.86348	+	7.86734i	−0.113993	+	0.313194i	−0.983549	−	0.180641i	$-0.942183\pi$
$631$	−2.86348	+	7.86734i	−0.113993	+	0.313194i	0.869556	+	0.493834i	$0.164405\pi$
$632$		0			0
$633$	−1.64985	−	1.38439i	−0.0655755	−	0.0550244i
$634$		0			0
$635$			16.6640i			0.661289i
$636$		0			0
$637$	9.54209	−	5.50913i	0.378071	−	0.218280i
$638$		0			0
$639$	−15.5512	+	26.9355i	−0.615196	+	1.06555i
$640$		0			0
$641$	11.1583	+	4.06129i	0.440726	+	0.160411i	0.552846	−	0.833283i	$-0.313542\pi$
$641$	11.1583	+	4.06129i	0.440726	+	0.160411i	−0.112120	+	0.993695i	$0.535764\pi$
$642$		0			0
$643$	33.5232	+	19.3547i	1.32203	+	0.763273i	0.984052	−	0.177882i	$-0.0569244\pi$
$643$	33.5232	+	19.3547i	1.32203	+	0.763273i	0.337976	+	0.941155i	$0.390258\pi$
$644$		0			0
$645$	0.593626	+	3.36662i	0.0233740	+	0.132561i
$646$		0			0
$647$	−6.03672	−	16.5857i	−0.237328	−	0.652053i	−0.999986	−	0.00525130i	$-0.998328\pi$
$647$	−6.03672	−	16.5857i	−0.237328	−	0.652053i	0.762658	−	0.646801i	$-0.223894\pi$
$648$		0			0
$649$	−19.6575	−	23.4269i	−0.771624	−	0.919586i
$650$		0			0
$651$	2.41799	−	0.426356i	0.0947683	−	0.0167102i
$652$		0			0
$653$	9.49773	−	11.3189i	0.371675	−	0.442945i	−0.547493	−	0.836810i	$-0.684418\pi$
$653$	9.49773	−	11.3189i	0.371675	−	0.442945i	0.919168	+	0.393865i	$0.128862\pi$
$654$		0			0
$655$	−13.6491	−	23.6410i	−0.533316	−	0.923731i
$656$		0			0
$657$	−7.83683	+	6.57588i	−0.305744	+	0.256550i
$658$		0			0
$659$	−1.14933	+	6.51815i	−0.0447714	+	0.253911i	−0.998976	−	0.0452437i	$-0.985594\pi$
$659$	−1.14933	+	6.51815i	−0.0447714	+	0.253911i	0.954205	+	0.299155i	$0.0967047\pi$
$660$		0			0
$661$	6.22992	+	1.09850i	0.242316	+	0.0427268i	0.293487	−	0.955963i	$-0.405184\pi$
$661$	6.22992	+	1.09850i	0.242316	+	0.0427268i	−0.0511712	+	0.998690i	$0.516295\pi$
$662$		0			0
$663$	1.29325	−	0.470703i	0.0502255	−	0.0182806i
$664$		0			0
$665$	−8.49307			−0.329347
$666$		0			0
$667$	−25.8340			−1.00030
$668$		0			0
$669$	0.273858	−	0.0996762i	0.0105880	−	0.00385370i
$670$		0			0
$671$	−57.4645	−	10.1325i	−2.21839	−	0.391163i
$672$		0			0
$673$	4.26450	−	24.1852i	0.164384	−	0.932269i	−0.785313	−	0.619099i	$-0.787498\pi$
$673$	4.26450	−	24.1852i	0.164384	−	0.932269i	0.949697	−	0.313170i	$-0.101391\pi$
$674$		0			0
$675$	2.84618	−	2.38822i	0.109549	−	0.0919228i
$676$		0			0
$677$	11.2322	+	19.4547i	0.431687	+	0.747704i	0.997019	−	0.0771600i	$-0.0245852\pi$
$677$	11.2322	+	19.4547i	0.431687	+	0.747704i	−0.565332	+	0.824864i	$0.691252\pi$
$678$		0			0
$679$	−21.7882	+	25.9662i	−0.836155	+	0.996491i
$680$		0			0
$681$	2.23123	−	0.393427i	0.0855011	−	0.0150762i
$682$		0			0
$683$	−21.2410	−	25.3140i	−0.812764	−	0.968614i	0.187142	−	0.982333i	$-0.440077\pi$
$683$	−21.2410	−	25.3140i	−0.812764	−	0.968614i	−0.999906	+	0.0137189i	$0.995633\pi$
$684$		0			0
$685$	−5.57496	−	15.3171i	−0.213008	−	0.585235i
$686$		0			0
$687$	0.398278	+	2.25875i	0.0151953	+	0.0861766i
$688$		0			0
$689$	−28.6222	−	16.5251i	−1.09042	−	0.629554i
$690$		0			0
$691$	32.8077	+	11.9410i	1.24806	+	0.454258i	0.879747	−	0.475442i	$-0.157712\pi$
$691$	32.8077	+	11.9410i	1.24806	+	0.454258i	0.368317	+	0.929700i	$0.379934\pi$
$692$		0			0
$693$	−17.9503	+	31.0909i	−0.681876	+	1.18104i
$694$		0			0
$695$	−15.5877	+	8.99954i	−0.591274	+	0.341372i
$696$		0			0
$697$		−	9.98299i		−	0.378133i
$698$		0			0
$699$	−6.01509	−	5.04726i	−0.227512	−	0.190905i
$700$		0			0
$701$	9.15308	−	25.1479i	0.345707	−	0.949823i	−0.637999	−	0.770037i	$-0.720237\pi$
$701$	9.15308	−	25.1479i	0.345707	−	0.949823i	0.983706	−	0.179785i	$-0.0575403\pi$
$702$		0			0
$703$	−2.68438	−	9.12735i	−0.101243	−	0.344245i
$704$		0			0
$705$	1.91544	−	5.26263i	0.0721397	−	0.198202i
$706$		0			0
$707$	6.53472	+	5.48328i	0.245763	+	0.206220i
$708$		0			0
$709$			6.67084i			0.250529i	0.992123	+	0.125264i	$0.0399779\pi$
$709$			6.67084i			0.250529i	−0.992123	+	0.125264i	$0.960022\pi$
$710$		0			0
$711$	6.35802	−	3.67081i	0.238444	−	0.137666i
$712$		0			0
$713$	10.8298	−	18.7578i	0.405580	−	0.702485i
$714$		0			0
$715$	60.5782	+	22.0487i	2.26550	+	0.824573i
$716$		0			0
$717$	−5.15738	−	2.97761i	−0.192606	−	0.111201i
$718$		0			0
$719$	−8.26991	−	46.9010i	−0.308416	−	1.74911i	−0.606975	−	0.794721i	$-0.707617\pi$
$719$	−8.26991	−	46.9010i	−0.308416	−	1.74911i	0.298559	−	0.954391i	$-0.403494\pi$
$720$		0			0
$721$	7.68026	+	21.1013i	0.286028	+	0.785855i
$722$		0			0
$723$	−1.26968	−	1.51314i	−0.0472198	−	0.0562743i
$724$		0			0
$725$	−7.26679	+	1.28133i	−0.269882	+	0.0475874i
$726$		0			0
$727$	32.2308	−	38.4112i	1.19537	−	1.42459i	0.315802	−	0.948825i	$-0.397726\pi$
$727$	32.2308	−	38.4112i	1.19537	−	1.42459i	0.879572	−	0.475766i	$-0.157829\pi$
$728$		0			0
$729$	10.3516	+	17.9296i	0.383394	+	0.664058i
$730$		0			0
$731$	−2.77931	+	2.33212i	−0.102796	+	0.0862565i
$732$		0			0
$733$	4.88298	−	27.6927i	0.180357	−	1.02285i	−0.751420	−	0.659824i	$-0.770631\pi$
$733$	4.88298	−	27.6927i	0.180357	−	1.02285i	0.931777	−	0.363031i	$-0.118258\pi$
$734$		0			0
$735$	−2.39039	−	0.421490i	−0.0881708	−	0.0155469i
$736$		0			0
$737$	59.4657	−	21.6438i	2.19045	−	0.797258i
$738$		0			0
$739$	−32.3511			−1.19006			−0.595028	−	0.803705i	$-0.702859\pi$
$739$	−32.3511			−1.19006			−0.595028	+	0.803705i	$0.702859\pi$
$740$		0			0
$741$	2.23632			0.0821533
$742$		0			0
$743$	7.05630	−	2.56828i	0.258871	−	0.0942212i	−0.209325	−	0.977846i	$-0.567127\pi$
$743$	7.05630	−	2.56828i	0.258871	−	0.0942212i	0.468195	+	0.883625i	$0.344904\pi$
$744$		0			0
$745$	8.98851	+	1.58492i	0.329313	+	0.0580668i
$746$		0			0
$747$	3.45801	−	19.6113i	0.126522	−	0.717542i
$748$		0			0
$749$	−32.3441	+	27.1399i	−1.18183	+	0.991672i
$750$		0			0
$751$	7.37086	+	12.7667i	0.268966	+	0.465863i	0.968595	−	0.248643i	$-0.0799846\pi$
$751$	7.37086	+	12.7667i	0.268966	+	0.465863i	−0.699629	+	0.714506i	$0.746651\pi$
$752$		0			0
$753$	−5.65884	+	6.74395i	−0.206220	+	0.245763i
$754$		0			0
$755$	−24.1966	+	4.26651i	−0.880603	+	0.155274i
$756$		0			0
$757$	−14.2111	−	16.9361i	−0.516511	−	0.615553i	0.443241	−	0.896402i	$-0.353828\pi$
$757$	−14.2111	−	16.9361i	−0.516511	−	0.615553i	−0.959752	+	0.280849i	$0.909384\pi$
$758$		0			0
$759$	−4.53736	−	12.4663i	−0.164696	−	0.452498i
$760$		0			0
$761$	5.52983	+	31.3612i	0.200456	+	1.13684i	0.904431	+	0.426619i	$0.140296\pi$
$761$	5.52983	+	31.3612i	0.200456	+	1.13684i	−0.703975	+	0.710225i	$0.748593\pi$
$762$		0			0
$763$	−11.2185	−	6.47698i	−0.406135	−	0.234482i
$764$		0			0
$765$	6.80119	+	2.47543i	0.245897	+	0.0894993i
$766$		0			0
$767$	−10.4986	+	18.1841i	−0.379082	+	0.656589i
$768$		0			0
$769$	19.6375	−	11.3377i	0.708148	−	0.408849i	−0.102227	−	0.994761i	$-0.532597\pi$
$769$	19.6375	−	11.3377i	0.708148	−	0.408849i	0.810375	+	0.585912i	$0.199263\pi$
$770$		0			0
$771$			1.79585i			0.0646761i
$772$		0			0
$773$	9.05550	+	7.59846i	0.325704	+	0.273298i	0.790947	−	0.611885i	$-0.209589\pi$
$773$	9.05550	+	7.59846i	0.325704	+	0.273298i	−0.465243	+	0.885183i	$0.654033\pi$
$774$		0			0
$775$	2.11593	−	5.81348i	0.0760066	−	0.208826i
$776$		0			0
$777$	0.488790	+	4.36539i	0.0175352	+	0.156607i
$778$		0			0
$779$	5.54818	−	15.2435i	0.198784	−	0.546155i
$780$		0			0
$781$	49.6162	+	41.6329i	1.77541	+	1.48974i
$782$		0			0
$783$			8.28033i			0.295915i
$784$		0			0
$785$	5.73241	−	3.30961i	0.204598	−	0.118125i
$786$		0			0
$787$	4.07295	−	7.05455i	0.145185	−	0.251468i	−0.784257	−	0.620436i	$-0.786956\pi$
$787$	4.07295	−	7.05455i	0.145185	−	0.251468i	0.929442	+	0.368969i	$0.120289\pi$
$788$		0			0
$789$	3.15649	+	1.14887i	0.112374	+	0.0409009i
$790$		0			0
$791$	−11.0423	−	6.37525i	−0.392618	−	0.226678i
$792$		0			0
$793$	6.95695	+	39.4548i	0.247049	+	1.40108i
$794$		0			0
$795$	2.49017	+	6.84168i	0.0883171	+	0.242649i
$796$		0			0
$797$	−16.0737	−	19.1558i	−0.569358	−	0.678535i	0.402141	−	0.915578i	$-0.368266\pi$
$797$	−16.0737	−	19.1558i	−0.569358	−	0.678535i	−0.971499	+	0.237043i	$0.923822\pi$
$798$		0			0
$799$	5.85340	−	1.03211i	0.207079	−	0.0365135i
$800$		0			0
$801$	30.1011	−	35.8731i	1.06357	−	1.26751i
$802$		0			0
$803$	10.6520	+	18.4499i	0.375902	+	0.651081i
$804$		0			0
$805$	26.4994	−	22.2357i	0.933982	−	0.783704i
$806$		0			0
$807$	−1.43993	+	8.16625i	−0.0506880	+	0.287466i
$808$		0			0
$809$	6.92526	+	1.22111i	0.243479	+	0.0429319i	0.294056	−	0.955788i	$-0.404995\pi$
$809$	6.92526	+	1.22111i	0.243479	+	0.0429319i	−0.0505767	+	0.998720i	$0.516106\pi$
$810$		0			0
$811$	−7.62149	+	2.77399i	−0.267627	+	0.0974081i	−0.472348	−	0.881412i	$-0.656593\pi$
$811$	−7.62149	+	2.77399i	−0.267627	+	0.0974081i	0.204721	+	0.978820i	$0.434371\pi$
$812$		0			0
$813$	−6.35860			−0.223006
$814$		0			0
$815$	24.4899			0.857845
$816$		0			0
$817$	−5.53997	+	2.01638i	−0.193819	+	0.0705443i
$818$		0			0
$819$	24.2747	+	4.28028i	0.848227	+	0.149565i
$820$		0			0
$821$	−8.00236	+	45.3837i	−0.279284	+	1.58390i	0.445730	+	0.895167i	$0.352944\pi$
$821$	−8.00236	+	45.3837i	−0.279284	+	1.58390i	−0.725015	+	0.688733i	$0.758167\pi$
$822$		0			0
$823$	−9.04503	+	7.58968i	−0.315290	+	0.264560i	−0.786674	−	0.617368i	$-0.788199\pi$
$823$	−9.04503	+	7.58968i	−0.315290	+	0.264560i	0.471384	+	0.881928i	$0.343754\pi$
$824$		0			0
$825$	−1.89462	−	3.28157i	−0.0659621	−	0.114250i
$826$		0			0
$827$	−18.3297	+	21.8445i	−0.637387	+	0.759608i	−0.983955	−	0.178417i	$-0.942902\pi$
$827$	−18.3297	+	21.8445i	−0.637387	+	0.759608i	0.346568	+	0.938025i	$0.387347\pi$
$828$		0			0
$829$	0.266399	−	0.0469734i	0.00925242	−	0.00163145i	−0.169020	−	0.985613i	$-0.554060\pi$
$829$	0.266399	−	0.0469734i	0.00925242	−	0.00163145i	0.178272	+	0.983981i	$0.442949\pi$
$830$		0			0
$831$	3.95838	+	4.71741i	0.137315	+	0.163645i
$832$		0			0
$833$	−0.881066	−	2.42071i	−0.0305271	−	0.0838726i
$834$		0			0
$835$	4.72629	+	26.8041i	0.163560	+	0.927595i
$836$		0			0
$837$	−6.01226	−	3.47118i	−0.207814	−	0.119982i
$838$		0			0
$839$	21.9497	+	7.98904i	0.757788	+	0.275812i	0.691879	−	0.722013i	$-0.256783\pi$
$839$	21.9497	+	7.98904i	0.757788	+	0.275812i	0.0659091	+	0.997826i	$0.479005\pi$
$840$		0			0
$841$	−6.27756	+	10.8731i	−0.216468	+	0.374933i
$842$		0			0
$843$	4.58622	−	2.64786i	0.157958	−	0.0911970i
$844$		0			0
$845$		−	10.3133i		−	0.354788i
$846$		0			0
$847$	39.7490	+	33.3534i	1.36579	+	1.14604i
$848$		0			0
$849$	2.90461	−	7.98034i	0.0996858	−	0.273885i
$850$		0			0
$851$	32.2719	+	21.4505i	1.10627	+	0.735314i
$852$		0			0
$853$	−6.83552	+	18.7804i	−0.234044	+	0.643030i	0.765956	+	0.642893i	$0.222266\pi$
$853$	−6.83552	+	18.7804i	−0.234044	+	0.643030i	−1.00000		0.000137243i	$0.999956\pi$
$854$		0			0
$855$	9.00930	+	7.55970i	0.308112	+	0.258536i
$856$		0			0
$857$			16.1108i			0.550334i	0.961396	+	0.275167i	$0.0887331\pi$
$857$			16.1108i			0.550334i	−0.961396	+	0.275167i	$0.911267\pi$
$858$		0			0
$859$	2.89285	−	1.67019i	0.0987029	−	0.0569861i	−0.449836	−	0.893111i	$-0.648518\pi$
$859$	2.89285	−	1.67019i	0.0987029	−	0.0569861i	0.548539	+	0.836125i	$0.315184\pi$
$860$		0			0
$861$	−3.74488	+	6.48633i	−0.127625	+	0.221054i
$862$		0			0
$863$	36.4573	+	13.2694i	1.24102	+	0.451695i	0.877359	−	0.479835i	$-0.159303\pi$
$863$	36.4573	+	13.2694i	1.24102	+	0.451695i	0.363664	+	0.931530i	$0.381526\pi$
$864$		0			0
$865$	−6.62596	−	3.82550i	−0.225289	−	0.130071i
$866$		0			0
$867$	0.969351	+	5.49747i	0.0329209	+	0.186704i
$868$		0			0
$869$	−5.22900	−	14.3666i	−0.177382	−	0.487352i
$870$		0			0
$871$	−27.9286	−	33.2840i	−0.946323	−	1.12778i
$872$		0			0
$873$	46.2252	−	8.15074i	1.56448	−	0.275861i
$874$		0			0
$875$	−11.1008	+	13.2295i	−0.375277	+	0.447238i
$876$		0			0
$877$	1.42022	+	2.45989i	0.0479573	+	0.0830644i	0.889008	−	0.457892i	$-0.151396\pi$
$877$	1.42022	+	2.45989i	0.0479573	+	0.0830644i	−0.841050	+	0.540957i	$0.818062\pi$
$878$		0			0
$879$	3.34485	−	2.80666i	0.112819	−	0.0946663i
$880$		0			0
$881$	−8.77517	+	49.7665i	−0.295643	+	1.67668i	0.368934	+	0.929456i	$0.379723\pi$
$881$	−8.77517	+	49.7665i	−0.295643	+	1.67668i	−0.664577	+	0.747220i	$0.731388\pi$
$882$		0			0
$883$	−28.2429	−	4.97998i	−0.950448	−	0.167590i	−0.323132	−	0.946354i	$-0.604736\pi$
$883$	−28.2429	−	4.97998i	−0.950448	−	0.167590i	−0.627317	+	0.778764i	$0.715847\pi$
$884$		0			0
$885$	4.34661	−	1.58204i	0.146110	−	0.0531796i
$886$		0			0
$887$	14.6784			0.492851			0.246425	−	0.969162i	$-0.420744\pi$
$887$	14.6784			0.492851			0.246425	+	0.969162i	$0.420744\pi$
$888$		0			0
$889$	13.2686			0.445015
$890$		0			0
$891$	44.6766	−	16.2610i	1.49672	−	0.544763i
$892$		0			0
$893$	9.51145	+	1.67713i	0.318289	+	0.0561229i
$894$		0			0
$895$	3.97560	−	22.5467i	0.132889	−	0.753654i
$896$		0			0
$897$	−6.97760	+	5.85490i	−0.232975	+	0.195489i
$898$		0			0
$899$	6.89383	+	11.9405i	0.229922	+	0.398237i
$900$		0			0
$901$	−4.96689	+	5.91931i	−0.165471	+	0.197201i
$902$		0			0
$903$	2.68066	−	0.472673i	0.0892068	−	0.0157296i
$904$		0			0
$905$	−44.9130	−	53.5252i	−1.49296	−	1.77924i
$906$		0			0
$907$	−15.3162	−	42.0808i	−0.508565	−	1.39727i	−0.882717	−	0.469904i	$-0.844289\pi$
$907$	−15.3162	−	42.0808i	−0.508565	−	1.39727i	0.374152	−	0.927367i	$-0.377934\pi$
$908$		0			0
$909$	−2.05124	−	11.6331i	−0.0680352	−	0.385847i
$910$		0			0
$911$	−5.76500	−	3.32842i	−0.191003	−	0.110276i	0.401449	−	0.915881i	$-0.368507\pi$
$911$	−5.76500	−	3.32842i	−0.191003	−	0.110276i	−0.592452	+	0.805606i	$0.701840\pi$
$912$		0			0
$913$	−38.9688	−	14.1835i	−1.28968	−	0.469405i
$914$		0			0
$915$	4.41289	−	7.64334i	0.145886	−	0.252681i
$916$		0			0
$917$	−18.8241	+	10.8681i	−0.621626	+	0.358896i
$918$		0			0
$919$			44.6670i			1.47343i	0.676203	+	0.736715i	$0.263624\pi$
$919$			44.6670i			1.47343i	−0.676203	+	0.736715i	$0.736376\pi$
$920$		0			0
$921$	−2.50137	−	2.09889i	−0.0824228	−	0.0691609i
$922$		0			0
$923$	15.2097	−	41.7884i	0.500634	−	1.37548i
$924$		0			0
$925$	10.1416	+	4.43313i	0.333454	+	0.145760i
$926$		0			0
$927$	10.6353	−	29.2202i	0.349308	−	0.959717i
$928$		0			0
$929$	1.25524	+	1.05327i	0.0411831	+	0.0345567i	0.663147	−	0.748489i	$-0.269220\pi$
$929$	1.25524	+	1.05327i	0.0411831	+	0.0345567i	−0.621964	+	0.783046i	$0.713665\pi$
$930$		0			0
$931$		−	4.18596i		−	0.137189i
$932$		0			0
$933$	−4.84279	+	2.79599i	−0.158546	+	0.0915365i
$934$		0			0
$935$	7.53606	−	13.0528i	0.246456	−	0.426874i
$936$		0			0
$937$	36.9995	+	13.4667i	1.20872	+	0.439938i	0.866260	−	0.499594i	$-0.166517\pi$
$937$	36.9995	+	13.4667i	1.20872	+	0.439938i	0.342461	+	0.939532i	$0.388740\pi$
$938$		0			0
$939$	−0.173230	−	0.100014i	−0.00565315	−	0.00326385i
$940$		0			0
$941$	−5.32651	−	30.2081i	−0.173639	−	0.984757i	−0.939703	−	0.341992i	$-0.888898\pi$
$941$	−5.32651	−	30.2081i	−0.173639	−	0.984757i	0.766064	−	0.642765i	$-0.222213\pi$
$942$		0			0
$943$	22.5979	+	62.0873i	0.735890	+	2.02184i
$944$		0			0
$945$	−7.12699	−	8.49361i	−0.231841	−	0.276297i
$946$		0			0
$947$	21.6531	−	3.81803i	0.703632	−	0.124069i	0.189626	−	0.981856i	$-0.439272\pi$
$947$	21.6531	−	3.81803i	0.703632	−	0.124069i	0.514005	+	0.857787i	$0.328161\pi$
$948$		0			0
$949$	9.40221	−	11.2051i	0.305209	−	0.363734i
$950$		0			0
$951$	−2.04083	−	3.53482i	−0.0661784	−	0.114624i
$952$		0			0
$953$	10.5688	−	8.86830i	0.342358	−	0.287272i	−0.455355	−	0.890310i	$-0.650488\pi$
$953$	10.5688	−	8.86830i	0.342358	−	0.287272i	0.797713	+	0.603038i	$0.206043\pi$
$954$		0			0
$955$	−0.824219	+	4.67438i	−0.0266711	+	0.151259i
$956$		0			0
$957$	8.31654	+	1.46643i	0.268835	+	0.0474029i
$958$		0			0
$959$	−12.1962	+	4.43904i	−0.393835	+	0.143344i
$960$		0			0
$961$	19.4402			0.627103
$962$		0			0
$963$	58.4674			1.88409
$964$		0			0
$965$	2.61358	−	0.951267i	0.0841342	−	0.0306224i
$966$		0			0
$967$	42.1185	+	7.42663i	1.35444	+	0.238824i	0.803293	−	0.595584i	$-0.203079\pi$
$967$	42.1185	+	7.42663i	1.35444	+	0.238824i	0.551147	+	0.834408i	$0.314190\pi$
$968$		0			0
$969$	0.0907921	−	0.514908i	0.00291666	−	0.0165412i
$970$		0			0
$971$	−42.7120	+	35.8396i	−1.37069	+	1.15015i	−0.398178	+	0.917308i	$0.630357\pi$
$971$	−42.7120	+	35.8396i	−1.37069	+	1.15015i	−0.972515	+	0.232840i	$0.925198\pi$
$972$		0			0
$973$	7.16585	+	12.4116i	0.229727	+	0.397898i
$974$		0			0
$975$	−1.67232	+	1.99299i	−0.0535570	+	0.0638268i
$976$		0			0
$977$	−18.0002	+	3.17393i	−0.575878	+	0.101543i	−0.453999	−	0.891002i	$-0.650003\pi$
$977$	−18.0002	+	3.17393i	−0.575878	+	0.101543i	−0.121879	+	0.992545i	$0.538892\pi$
$978$		0			0
$979$	−62.6842	−	74.7042i	−2.00340	−	2.38756i
$980$		0			0
$981$	6.13517	+	16.8563i	0.195881	+	0.538179i
$982$		0			0
$983$	4.37560	+	24.8153i	0.139560	+	0.791485i	0.971575	+	0.236731i	$0.0760762\pi$
$983$	4.37560	+	24.8153i	0.139560	+	0.791485i	−0.832015	+	0.554753i	$0.812813\pi$
$984$		0			0
$985$	35.6348	+	20.5738i	1.13542	+	0.655534i
$986$		0			0
$987$	−4.19035	−	1.52516i	−0.133380	−	0.0485465i
$988$		0			0
$989$	12.0063	−	20.7955i	0.381778	−	0.661259i
$990$		0			0
$991$	25.7428	−	14.8626i	0.817748	−	0.472127i	−0.0318914	−	0.999491i	$-0.510153\pi$
$991$	25.7428	−	14.8626i	0.817748	−	0.472127i	0.849639	+	0.527364i	$0.176820\pi$
$992$		0			0
$993$		−	4.90989i		−	0.155811i
$994$		0			0
$995$	−41.2840	−	34.6414i	−1.30879	−	1.09820i
$996$		0			0
$997$	−3.03661	+	8.34301i	−0.0961703	+	0.264226i	−0.978444	−	0.206510i	$-0.933789\pi$
$997$	−3.03661	+	8.34301i	−0.0961703	+	0.264226i	0.882274	+	0.470736i	$0.156012\pi$
$998$		0			0
$999$	6.87533	−	10.3438i	0.217526	−	0.327264i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	592.2.bq.b.465.2		12
4.3	odd	2		74.2.h.a.21.1	✓	12
12.11	even	2		666.2.bj.c.613.2		12
37.30	even	18	inner	592.2.bq.b.289.2		12
148.67	odd	18		74.2.h.a.67.1	yes	12
148.91	even	36		2738.2.a.r.1.3		6
148.131	even	36		2738.2.a.s.1.4		6
444.215	even	18		666.2.bj.c.289.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.2.h.a.21.1	✓	12	4.3	odd	2
74.2.h.a.67.1	yes	12	148.67	odd	18
592.2.bq.b.289.2		12	37.30	even	18	inner
592.2.bq.b.465.2		12	1.1	even	1	trivial
666.2.bj.c.289.2		12	444.215	even	18
666.2.bj.c.613.2		12	12.11	even	2
2738.2.a.r.1.3		6	148.91	even	36
2738.2.a.s.1.4		6	148.131	even	36

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 592 = 2^{4} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	592.bq (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.326352 + 0.118782i) q^{3} +(2.57176 + 0.453471i) q^{5} +(0.361075 - 2.04776i) q^{7} +(-2.20574 + 1.85083i) q^{9} +O(q^{10})\)	\(q+(-0.326352 + 0.118782i) q^{3} +(2.57176 + 0.453471i) q^{5} +(0.361075 - 2.04776i) q^{7} +(-2.20574 + 1.85083i) q^{9} +(2.99810 + 5.19285i) q^{11} +(2.64632 - 3.15377i) q^{13} +(-0.893164 + 0.157489i) q^{15} +(-0.618710 - 0.737350i) q^{17} +(-0.534946 - 1.46975i) q^{19} +(0.125400 + 0.711179i) q^{21} +(5.51705 + 3.18527i) q^{23} +(1.70986 + 0.622339i) q^{25} +(1.02094 - 1.76833i) q^{27} +(-3.51193 + 2.02761i) q^{29} -3.39997i q^{31} +(-1.59525 - 1.33858i) q^{33} +(1.85720 - 5.10261i) q^{35} +(6.07068 + 0.383130i) q^{37} +(-0.489021 + 1.34357i) q^{39} +(7.94502 + 6.66666i) q^{41} -3.76932i q^{43} +(-6.51193 + 3.75967i) q^{45} +(-3.08750 + 5.34771i) q^{47} +(2.51491 + 0.915354i) q^{49} +(0.289501 + 0.167144i) q^{51} +(-1.39401 - 7.90585i) q^{53} +(5.35558 + 14.7143i) q^{55} +(0.349161 + 0.416114i) q^{57} +(-5.02269 + 0.885636i) q^{59} +(-6.25519 + 7.45465i) q^{61} +(2.99362 + 5.18510i) q^{63} +(8.23586 - 6.91071i) q^{65} +(1.83263 - 10.3934i) q^{67} +(-2.17885 - 0.384190i) q^{69} +(10.1503 - 3.69442i) q^{71} +3.55293 q^{73} -0.631940 q^{75} +(11.7162 - 4.26436i) q^{77} +(-2.51098 - 0.442753i) q^{79} +(1.37686 - 7.80856i) q^{81} +(-5.29798 + 4.44553i) q^{83} +(-1.25681 - 2.17686i) q^{85} +(0.905280 - 1.07887i) q^{87} +(-16.0165 + 2.82414i) q^{89} +(-5.50263 - 6.55778i) q^{91} +(0.403856 + 1.10959i) q^{93} +(-0.709264 - 4.02243i) q^{95} +(-14.1175 - 8.15074i) q^{97} +(-16.2241 - 5.90509i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{3} + 12 q^{7} - 6 q^{9}+O(q^{10}) \) 12 * q - 6 * q^3 + 12 * q^7 - 6 * q^9	\( 12 q - 6 q^{3} + 12 q^{7} - 6 q^{9} + 6 q^{11} + 6 q^{13} + 18 q^{19} - 6 q^{21} - 18 q^{25} + 6 q^{27} + 18 q^{29} - 6 q^{33} - 18 q^{35} + 30 q^{37} - 30 q^{39} + 24 q^{41} - 18 q^{45} - 6 q^{47} + 12 q^{49} - 12 q^{53} + 18 q^{55} - 36 q^{57} - 36 q^{61} + 6 q^{63} + 36 q^{65} + 30 q^{67} - 18 q^{69} - 12 q^{71} + 36 q^{75} + 12 q^{77} - 6 q^{79} + 24 q^{81} + 48 q^{83} + 18 q^{85} - 36 q^{87} - 18 q^{89} + 6 q^{91} - 12 q^{93} + 36 q^{97} - 30 q^{99}+O(q^{100}) \) 12 * q - 6 * q^3 + 12 * q^7 - 6 * q^9 + 6 * q^11 + 6 * q^13 + 18 * q^19 - 6 * q^21 - 18 * q^25 + 6 * q^27 + 18 * q^29 - 6 * q^33 - 18 * q^35 + 30 * q^37 - 30 * q^39 + 24 * q^41 - 18 * q^45 - 6 * q^47 + 12 * q^49 - 12 * q^53 + 18 * q^55 - 36 * q^57 - 36 * q^61 + 6 * q^63 + 36 * q^65 + 30 * q^67 - 18 * q^69 - 12 * q^71 + 36 * q^75 + 12 * q^77 - 6 * q^79 + 24 * q^81 + 48 * q^83 + 18 * q^85 - 36 * q^87 - 18 * q^89 + 6 * q^91 - 12 * q^93 + 36 * q^97 - 30 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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